II. GEOMETRIC RELATIONS

II. GEOMETRIC RELATIONS

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WHAT IS AN ANGLE?

Here some examples of angles:

Two rays that share the same endpoint form an angle. The point where the rays intersect is called the vertex of the angle. The two rays are called the sides of the angle.

          We can specify an angle by using a point on each ray and the vertex. The angle below may be specified as angle ABC or as angle CBA; you may also see this written as ABC or as CBA. Note how the vertex point is always given in the middle.

          How to measure an angle?

          We measure the size of an angle using degrees.

Angles are classified into three kinds: acute angle, right angle, and obtuse angle.

KINDS OF ANGLES

ACUTE ANGLE

An acute angle is an angle measuring between 0 and 90 degrees.

RIGHT ANGLE

A right angle is an angle measuring 90 degrees. Two lines or line segments that meet at a right angle are said to be perpendicular. Note that any two right angles are supplementary angles (a right angle is its own angle supplement).

Example:

OBTUSE ANGLE

An obtuse angle is an angle measuring between 90 and 180 degrees.

Example:

PAIRS OF ANGLES

COMPLEMENTARY ANGLES

Two angles are called complementary angles if the sum of their degree measurements equals 90 degrees. One of the complementary angles is said to be the complement of the other.

Notice that these two angles can be "pasted" together to form a right angle!

SUPPLEMENTARY ANGLES

Two angles are called supplementary angles if the sum of their degree measurements equals 180 degrees. One of the supplementary angles is said to be the supplement of the other.

Notice that these two angles can be "pasted" together to form a straight line!

VERTICAL ANGLES

For any two lines that meet, such as in the diagram below, angle AEB and angle DEC are called vertical angles. Vertical angles have the same degree measurement. Angle BEC and angle AED are also vertical angles.

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